The lattice of trumping majorization for 4D probability vectors and 2D catalysts

Autores
Bosyk, Gustavo Martin; Freytes Solari, Hector Carlos; Bellomo, Guido; Sergioli, Giuseppe
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The transformation of an initial bipartite pure state into a target one by means of local operations and classical communication and entangled-assisted by a catalyst defines a partial order between probability vectors. This partial order, so-called trumping majorization, is based on tensor products and the majorization relation. Here, we aim to study order properties of trumping majorization. We show that the trumping majorization partial order is indeed a lattice for four dimensional probability vectors and two dimensional catalysts. In addition, we show that the subadditivity and supermodularity of the Shannon entropy on the majorization lattice are inherited by the trumping majorization lattice. Finally, we provide a suitable definition of distance for four dimensional probability vectors.
Fil: Bosyk, Gustavo M.. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina
Fil: Freytes, Hector. Universita Degli Studi Di Cagliari; Italia
Fil: Bellomo, Guido. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación En Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación En Ciencias de la Computacion; Argentina
Fil: Sergioli, Giuseppe. Universita Degli Studi Di Cagliari; Italia
Materia
Local operations and classical communication
Entanglement-assisted transformations
Trumping majorization
Lattice
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/95925
Acceder
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network_name_str CONICET Digital (CONICET)
spelling The lattice of trumping majorization for 4D probability vectors and 2D catalystsBosyk, Gustavo MartinFreytes Solari, Hector CarlosBellomo, GuidoSergioli, GiuseppeLocal operations and classical communicationEntanglement-assisted transformationsTrumping majorizationLatticehttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1The transformation of an initial bipartite pure state into a target one by means of local operations and classical communication and entangled-assisted by a catalyst defines a partial order between probability vectors. This partial order, so-called trumping majorization, is based on tensor products and the majorization relation. Here, we aim to study order properties of trumping majorization. We show that the trumping majorization partial order is indeed a lattice for four dimensional probability vectors and two dimensional catalysts. In addition, we show that the subadditivity and supermodularity of the Shannon entropy on the majorization lattice are inherited by the trumping majorization lattice. Finally, we provide a suitable definition of distance for four dimensional probability vectors.Fil: Bosyk, Gustavo M.. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; ArgentinaFil: Freytes, Hector. Universita Degli Studi Di Cagliari; ItaliaFil: Bellomo, Guido. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación En Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación En Ciencias de la Computacion; ArgentinaFil: Sergioli, Giuseppe. Universita Degli Studi Di Cagliari; ItaliaNature Publishing Group2018-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/95925Bosyk, Gustavo Martin; Freytes Solari, Hector Carlos; Bellomo, Guido; Sergioli, Giuseppe; The lattice of trumping majorization for 4D probability vectors and 2D catalysts; Nature Publishing Group; Scientific Reports; 8; 3671 ; 12-2018; 1-82045-2322CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1038/s41598-018-21947-0info:eu-repo/semantics/altIdentifier/url/https://www.nature.com/articles/s41598-018-21947-0info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:03:10Zoai:ri.conicet.gov.ar:11336/95925instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-22 11:03:10.918CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The lattice of trumping majorization for 4D probability vectors and 2D catalysts
title The lattice of trumping majorization for 4D probability vectors and 2D catalysts
spellingShingle The lattice of trumping majorization for 4D probability vectors and 2D catalysts
Bosyk, Gustavo Martin
Local operations and classical communication
Entanglement-assisted transformations
Trumping majorization
Lattice
title_short The lattice of trumping majorization for 4D probability vectors and 2D catalysts
title_full The lattice of trumping majorization for 4D probability vectors and 2D catalysts
title_fullStr The lattice of trumping majorization for 4D probability vectors and 2D catalysts
title_full_unstemmed The lattice of trumping majorization for 4D probability vectors and 2D catalysts
title_sort The lattice of trumping majorization for 4D probability vectors and 2D catalysts
dc.creator.none.fl_str_mv Bosyk, Gustavo Martin
Freytes Solari, Hector Carlos
Bellomo, Guido
Sergioli, Giuseppe
author Bosyk, Gustavo Martin
author_facet Bosyk, Gustavo Martin
Freytes Solari, Hector Carlos
Bellomo, Guido
Sergioli, Giuseppe
author_role author
author2 Freytes Solari, Hector Carlos
Bellomo, Guido
Sergioli, Giuseppe
author2_role author
author
author
dc.subject.none.fl_str_mv Local operations and classical communication
Entanglement-assisted transformations
Trumping majorization
Lattice
topic Local operations and classical communication
Entanglement-assisted transformations
Trumping majorization
Lattice
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The transformation of an initial bipartite pure state into a target one by means of local operations and classical communication and entangled-assisted by a catalyst defines a partial order between probability vectors. This partial order, so-called trumping majorization, is based on tensor products and the majorization relation. Here, we aim to study order properties of trumping majorization. We show that the trumping majorization partial order is indeed a lattice for four dimensional probability vectors and two dimensional catalysts. In addition, we show that the subadditivity and supermodularity of the Shannon entropy on the majorization lattice are inherited by the trumping majorization lattice. Finally, we provide a suitable definition of distance for four dimensional probability vectors.
Fil: Bosyk, Gustavo M.. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina
Fil: Freytes, Hector. Universita Degli Studi Di Cagliari; Italia
Fil: Bellomo, Guido. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación En Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación En Ciencias de la Computacion; Argentina
Fil: Sergioli, Giuseppe. Universita Degli Studi Di Cagliari; Italia
description The transformation of an initial bipartite pure state into a target one by means of local operations and classical communication and entangled-assisted by a catalyst defines a partial order between probability vectors. This partial order, so-called trumping majorization, is based on tensor products and the majorization relation. Here, we aim to study order properties of trumping majorization. We show that the trumping majorization partial order is indeed a lattice for four dimensional probability vectors and two dimensional catalysts. In addition, we show that the subadditivity and supermodularity of the Shannon entropy on the majorization lattice are inherited by the trumping majorization lattice. Finally, we provide a suitable definition of distance for four dimensional probability vectors.
publishDate 2018
dc.date.none.fl_str_mv 2018-12
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/95925
Bosyk, Gustavo Martin; Freytes Solari, Hector Carlos; Bellomo, Guido; Sergioli, Giuseppe; The lattice of trumping majorization for 4D probability vectors and 2D catalysts; Nature Publishing Group; Scientific Reports; 8; 3671 ; 12-2018; 1-8
2045-2322
CONICET Digital
CONICET
url http://hdl.handle.net/11336/95925
identifier_str_mv Bosyk, Gustavo Martin; Freytes Solari, Hector Carlos; Bellomo, Guido; Sergioli, Giuseppe; The lattice of trumping majorization for 4D probability vectors and 2D catalysts; Nature Publishing Group; Scientific Reports; 8; 3671 ; 12-2018; 1-8
2045-2322
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1038/s41598-018-21947-0
info:eu-repo/semantics/altIdentifier/url/https://www.nature.com/articles/s41598-018-21947-0
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Nature Publishing Group
publisher.none.fl_str_mv Nature Publishing Group
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.982451

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